Skip to main content

Research Repository

Advanced Search

Time domain analysis of Helmholtz soliton propagation using the TLM method

Chamorro-Posada, P; McDonald, GS

Authors

P Chamorro-Posada



Abstract

The transmission line matrix method is used to study Helmholtz solitons as solutions of the two-dimensional time-domain Maxwell equations in nonlinear media. This approach permits to address, in particular, the propagation and intrinsic stability properties of subwavelength soliton solutions of the scalar nonlinear wave equation and the behaviour of optical solitons at arbitrary interfaces. Various numerical issues related to the analysis of soliton beams using the time-domain method are also discussed.

Citation

Chamorro-Posada, P., & McDonald, G. (2012). Time domain analysis of Helmholtz soliton propagation using the TLM method. Journal of Nonlinear Optical Physics and Materials, 21(03), https://doi.org/10.1142/S0218863512500312

Journal Article Type Article
Publication Date Sep 1, 2012
Deposit Date Aug 8, 2014
Journal Journal of Nonlinear Optical Physics and Materials
Print ISSN 0218-8635
Electronic ISSN 1793-6624
Publisher World Scientific Publishing
Peer Reviewed Peer Reviewed
Volume 21
Issue 03
DOI https://doi.org/10.1142/S0218863512500312
Publisher URL http://dx.doi.org/10.1142/S0218863512500312
Additional Information References : 1. S. Trillo and W. Torruellas (eds.), Spatial Solitons, Springer Series in Optical Sciences (Springer-Verlag, 2010). 2. Y. S. Kivshar and G. P. Agrawal, Optical Solitons: From Fibers to Photonic Crystals (Academic Press, London, 2003). 3. T. R. Taha and M. J. Ablowitz, Analytical and numerical aspects of certain nonlinear evolution equations, II. numerical, nonlinear Schrodinger equation, J. Comput. Phys. 55 (2) (1984) 203. 4. P. Chamorro-Posada, G. S. McDonald and G. H. C. New, Nonparaxial solitons, J. Mod. Opt. 45 (6) (1998) 1111. 5. P. Chamorro-Posada, G. S. McDonald and G. H. C. New, Propagation properties of nonparaxial solitons, J. Mod. Opt. 47 (11) (2000) 1877. 6. P. Chamorro-Posada, G. S. McDonald and G. H. C. New, Exact soliton solutions of the nonlinear Helmholtz equation: Communication, J. Opt. Soc. Am. B 19 (2002) 1216. 7. P. Chamorro-Posada, G. S. McDonald and G. H. C. New, Nonparaxial beam propagation methods, Opt. Commun. 192 (2001) 1. 8. P. Chamorro-Posada and G. S. McDonald, Spatial Kerr soliton collisions at arbitrary angles, Phys. Rev. E 74 (2006) 36609. 9. J. M. Christian, G. S. McDonald and P. Chamorro-Posada, Helmholtz solitons in optical materials with a dual power-law nonlinearity, J. Nonlinear Opt. Phys. Mat. 19 (3) (2010) 389. 10. J. M. Christian, G. S. McDonald and P. Chamorro-Posada, Helmholtz algebraic solitons, J. Phys. A, Math. Theor. 43 (8) (2009) 085212. 11. J. M. Christian, G. S. McDonald and P. Chamorro-Posada, Bistable Helmholtz bright solitons in saturable materials, J. Opt. Soc. Am B 26 (12) (2009) 2302. 12. J. M. Christian, G. S. McDonald and R. J. Potton and P. Chamorro-Posada, Helmholtz solitons in power-law optical materials, Phys. Rev. A 76 (3) (2007) 033834. 13. J. M. Christian, G. S. McDonald and P. Chamorro-Posada, Bistable Helmholtz solitons in cubic-quintic materials, Phys. Rev. A 76 (3) (2007) 033833. 14. J. M. Christian, G. S. McDonald and P. Chamorro-Posada, Helmholtz bright and boundary solitons, J. Phys. A. Math. Theor. 40 (7) (2007) 1545. 15. J. Sanchez-Curto, P. Chamorro-Posada and G. S. McDonald, Giant Goos-Hanchen shifts and radiation-induced trapping of Helmholtz solitons at nonlinear interfaces, Opt. Lett. 36 (18) (2011) 3605. 16. J. Sanchez-Curto, P. Chamorro-Posada and G. S. McDonald, Helmholtz bright and black soliton splitting at nonlinear interfaces, Phys. Rev. A 85 (1) (2012) 013836. 17. J. Sanchez-Curto, P. Chamorro-Posada and G. S. McDonald, Nonlinear interfaces: Intrinsically nonparaxial regimes and effects, J. Opt. A, Pure Appl. Opt. 11 (5) (2009) 054015. 18. J. Sanchez-Curto, P. Chamorro-Posada and G. S. McDonald, Helmholtz soltions at nonlinear interfaces, Opt. Lett. 32 (9) (2007) 1126. 19. P. B. Johns and R. L. Beurle, Numerical solution of two-dimensional scattering problems using a transmission-line matrix, Proc. IEE 118 (9) (1971) 1203. 20. W. J. R. Hoefer, The transmission-line matrix method — Theory and applications, IEEE Trans. Microwave Theory Tech. MTT-33 (10) (1985) 882. 21. C. Christopoulos, The Transmission-line Matrix Method: TLM (IEEE Press, Piscataway, NJ, 1995). 22. C. Chen and S. Chi, Subwavelength spatial solitons of the TE mode, Opt. Commun. 157 (1998) 170. 23. E. Granot, S. Sternklar, Y. Isbi, B. Malomed and A. Lewis, On the existence of subwavelength spatial solitons, Opt. Commun. 178 (2000) 431. 24. P. M. Goorjian and Y. Silberberg, Numericalsimulations of light bullets using the full-vector time-dependent nonlinear Maxwell equations, J. Opt. Soc. Am. B 14 (11) (1997) 3253. 25. R. M. Joseph and A. Taflove, Spatial soliton deflection mechanism indicated by FD-TD Maxwell’s equations modeling, IEEE Photon. Technol. Lett. 6 (10) (1994) 1251. 26. A. D. Boardam, L. Velasco, Y. Papoport and N. King, Ultra-narrow bright spatial solitons interacting with left-handed surfaces, J. Opt. Soc. Am. B 22 (7) (2005) 1443. 27. R. M. Joseph, P. M. Goorjian and A. Taflove, Direct time integration of Maxwell’s equations in two-dimensional dielectric waveguides for propagation and scattering of femtosecond electromagnetic solitons, Opt. Lett. 18 (7) (1993) 491. 28. P. Chamorro-Posada, TLM analysis of multimode interference devices, Fiber Integrated Opt. 25 (1) (2006) 1. 29. P. B. Johns and M. O’Brien, Use of the transmission line modeling (T.L.M.) method to solve nonlinear lumped networks, Radio Electron. Eng. 50 (1&2) (1980) 59. 30. L. A. Newcombe and J. E. Sitch, Reactive nonlinearities in transmission-line models, IEE Proc.-A 132 (2) (1985) 95. 31. S. Y. R. Hui and C. Christopoulos, Discrete transform technique for solving nonlinear circuits and equations, IEE Proc.-A 139 (6) (1992) 321. 32. P. Russer, P. P. M. So and W. J. R. Hoefer, Modeling of nonlinear active regions in TLM, IEEE Microwave Guided Wave Lett. 1 (1) (1991) 10. 33. L. R. A. X. Menezes and W. J. R. Hoefer, Modeling of general constitutive relationships in SCN TLM, IEEE Trans. Microwave Theory Tech. 44 (6) (1996) 854. 34. J. Paul, C. Christopoulos and D. W. P. Thomas, Generalized material models in TLM — part 3: Materials with nonlinear properties, IEEE Trans. Antennas Propagat. 50 (7) (2002) 997. 35. V. Janyani, J. D. Paul, A. Vukovic, T. M. Benson and P. Sewell, TLM modelling of nonlinear optical effects in fibre Bragg gratings, IEE Proc.-J. 151 (4) (2004) 185.
Funders : Spanish Ministerio de Educacion y Ciencia;Junta de Castilla y Leon
Grant Number: TEC2010-21303-C04-0
Grant Number: VA300A12-1